Return the centroid of the moving body as a temporal point

centroid(trgeometry) → tgeompoint

SELECT asText(centroid( trgeometry 'Polygon((0 0, 1 0, 1 1, 0 1, 0 0));
  [Pose(Point(0 0),0)@2001-01-01, Pose(Point(2 0),0)@2001-01-02]'));
-- [POINT(0.5 0.5)@2001-01-01, POINT(2.5 0.5)@2001-01-02]

Return the convex hull of the area traversed by the moving body

convexHull(trgeometry) → geometry

SELECT ST_GeometryType(convexHull( trgeometry 'Polygon((0 0, 1 0, 1 1, 0 1, 0 0));
  [Pose(Point(0 0),0)@2001-01-01, Pose(Point(2 0),0)@2001-01-02]'));
-- ST_Polygon

Return the world-frame trajectory of a body-frame point carried by the moving rigid geometry

bodyPointTrajectory(trgeometry,geometry) → tgeompoint

The point is expressed in the reference shape's local frame and the time-varying pose is applied to it at each instant. The result has the interpolation of the temporal rigid geometry. With linear interpolation, the result is exact along a segment in which the body does not rotate. Along a segment in which the body rotates, the point follows a curve, which the result replaces by the segment joining its positions at the two instants, as in the second example below, where the point moves from (1 0) to (0 1) along a quarter of a circle.

SELECT asText(bodyPointTrajectory( trgeometry 'Polygon((0 0, 1 0, 1 1, 0 1, 0 0));
  [Pose(Point(0 0),0)@2001-01-01, Pose(Point(2 0),0)@2001-01-02]',
  geometry 'Point(0 0)'));
-- [POINT(0 0)@2001-01-01, POINT(2 0)@2001-01-02]
SELECT asText(round(bodyPointTrajectory( trgeometry 'Polygon((0 0, 1 0, 1 1, 0 1, 0 0));
  [Pose(Point(0 0),0)@2001-01-01, Pose(Point(0 0),1.5707963267948966)@2001-01-02]',
  geometry 'Point(1 0)'), 6));
-- [POINT(1 0)@2001-01-01, POINT(0 1)@2001-01-02]